Question: Simplify the following expression: $a = \dfrac{-10x^2 + 130x - 300}{x - 10} $
First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-10$ , so we can rewrite the expression: $ a =\dfrac{-10(x^2 - 13x + 30)}{x - 10} $ Then we factor the remaining polynomial: $x^2 {-13}x + {30} $ ${-10} {-3} = {-13}$ ${-10} \times {-3} = {30}$ $ (x {-10}) (x {-3}) $ This gives us a factored expression: $\dfrac{-10(x {-10}) (x {-3})}{x - 10}$ We can divide the numerator and denominator by $(x + 10)$ on condition that $x \neq 10$ Therefore $a = -10(x - 3); x \neq 10$